Graphics Programs Reference
In-Depth Information
Matrices
A
matrix
is a rectangular array of numbers. Row and column vectors, which
we discussed above, are examples of matrices. Consider the 3
×
4 matrix
1234
5678
9101112
.
A
=
It can be entered in MATLAB withthe command
>> A = [1, 2, 3, 4; 5, 6, 7, 8; 9, 10, 11, 12]
A=
1 2 3 4
5 6 7 8
9 0 1 2
Note that the matrix
elements
in any row are separated by commas, and the
rowsareseparatedbysemicolons.Theelementsinarowcanalsobeseparated
by spaces.
If two matrices
A
and
B
are the same size, their (element-by-element) sum
is obtained by typing
A+B
. You can also add a scalar (a single number) to a
matrix;
A+c
adds
c
to eachelement in
A
. Likewise,
A-B
represents the
difference of
A
and
B
, and
A-c
subtracts the number
c
from eachelement
of
A
.If
A
and
B
are multiplicatively compatible (that is, if
A
is
n
×
m
and
B
is
m
×
), then their product
A*B
is
n
×
. Recall that the element of
A*B
in the
i
throw and
j
th column is the sum of the products of the elements from the
i
throw of
A
times the elements from the
j
thcolumn of
B
, that is,
m
(
A
∗
B
)
ij
=
A
ik
B
kj
,
1
≤
i
≤
n
,
1
≤
j
≤
.
k
=
1
The product of a number
c
and the matrix
A
is given by
c*A
, and
A'
represents
the conjugate transpose of
A
. (For more information, see the online help for
ctranspose
and
transpose
.)
A simple illustration is given by the matrix product of the 3
×
4 matrix
A
above by the 4
×
1 column vector
Z'
:
>> A*Z'
ans =
60
140
220
Search WWH ::
Custom Search